Determine whether the Mean Value Theorem applies to f(x) = 3x – x^2 on the interval [2, 3]. If it can be applied, find all value(s) of c in the interval that satisfy the Mean Value Theorem.

This is what I did

I used my graphing calculator and found the intersection between f(c) and 7/6, and the answer is 2.5408.

Did I do it correctly? If I did, is there a way to do it without a calculator?